She pleaded guilty at the High Court in Auckland this week to a representative charge of wounding her daughter with intent to injure.
The baby was discharged from Starship, then recalled to hospital when police became "concerned at the lack of medical explanation for [the] episodes", say court documents.
Her daughter was taken into Child, Youth and Family care and now lives with her grandmother. Three months ago she revealed her second daughter had been born.
"She was taken away the day she was born. I wasn't allowed to breast-feed her or anything. She is also living with my mother-in-law and I am allowed see them twice a week.
"They are so beautiful. I have two nicknames for my oldest, Monkey and Princess.
"She's my bright sparkle."
Court documents state her first baby was born healthy at Waitakere Hospital in October 2010, but Broadbent told her midwife she struggled to cope and had thoughts of harming her child shortly after the birth.
"The defendant told the midwife she had got so frustrated with the baby that she had raised her fist above the baby's head," say the documents.
Broadbent said her partner took the baby out of the room before she punched the pillow.
When she told her midwife she had contemplated throwing the child out of a window, mental health workers put her on medication for post-natal depression.
Broadbent said her daughter was admitted to Waitakere Hospital after she stopped breathing at home about a month after her birth.
"I was screaming because baby was not breathing but my mother-in-law took action and started CPR," she said.
Court documents say Broadbent suffocated the child in Waitakere Hospital while breast-feeding, before pushing the emergency button. Nurses and doctors noticed blood around her mouth and nose.
She was sent to Starship Children's Hospital where she was classed as "very unwell".
Her daughter was discharged then recalled but Broadbent was not told why they had to go back to Starship.
While there, police say she again suffocated her baby. Despite pleading guilty, she still denies she did it.
"I was on the other bed about a metre away when I noticed she wasn't moving. When I saw her go blue around the mouth I pushed the emergency button."
A medical team resuscitated the little girl who was "floppy with no pulse".
A Waitemata DHB spokeswoman would not comment before sentencing.
